Tonearm Effective Mass & Cartridge Compliance

[Barry]

Michael,

The relationship between the effective mass of the tonearm and the cartridge compliance is essentially reciprocal. Ideally the product of the total mass of the arm and cartridge (plus any fixings), with the cartridge compliance should be such that the resonant frequency of the combination is ~10Hz. It therefore follows that one should match low compliance cartridges to arms having a high effective mass and vice versa.

If the resonant frequency is too low (< 8Hz), the arm cartridge combination will be subject to disturbance by record warps and possible turntable motor rumble, and if the turntable has a particularly ‘bouncy’ un-damped suspension, by footfalls. Another unwanted effect of placing the arm/cartridge resonance at too low a frequency, is that if excited, the large stylus deflections that can occur will lead to a form of intermodulation distortion via a mechanism called 'scrub flutter'. The latter is a modulation of the effective longitudinal groove velocity.

Conversely if the resonant frequency is too high (> 12Hz), recorded low frequency audio notes will affect the arm-cartridge combination. At resonance, the output can be up to as much as 15dB higher (i.e. 5 - 6 x), though this depends to some extent on the cartridge and on the arm. For example, if the arm-cartridge combination has a resonance of +15dB at 15Hz it will, depending on the Q-value of the resonance, cause the cartridge output to be lifted by up to +6db at 20Hz; so affecting the low frequency response of the audio system and possibly overloading the amplifier and loudspeakers.

If the resonant frequency is too low, mass needs to be removed, by using a tonearm having a lower effective mass. Alternatively a damper dashpot can be used with the tonearm. Use of such a damper will typically raise the resonant frequency by about 1.5Hz, as well as lower the Q-value at resonance.

If the resonant frequency is too high, additional mass can be added to the headshell to bring the frequency down.



To check this, simply multiply the cartridge compliance, C (in 'cu', that is, ignore the factor 10^-6), by the total mass, M (= the cartridge mass + the effective mass of the arm + the mass of the fixings used, in grams) and if the product lays between 175 and 400, the resonant frequency of the arm/cartridge combination will lay in the 'safe zone' of 8 - 12Hz.

So, for example, a cartridge having a mass of 9g and a compliance of 10cu, when fitted into an arm having an effective mass of 9.5g using fixings weighing 0.5g, the MC product will be (9 + 9.5 + 0.5) x 10 = 190. Since this lays within the range 175 - 400, the arm/cartidge combination is satisfactory and no problems should be encountered.